Neural Nets: CNN confirming layer/filter arithmetic
Your first point is correct. The filters are stored in 4d arrays, with dimensions of (height, width, input channels, filter number) . The order may differ.
Your second point is correct too. The filtered result get stacked together so the output dimensions are (Height,width,filter numbers) the next layer's filters are of size( filter width, filter width, last layer's filter number). Your understanding of CNN is correct. If you want additional resources on CNN, you can try Andrew Ng's class on CNN in Coursera. Hope you can learn more about CNN.